After a humbling 3-0 defeat by Manchester City this month, Iraola's side have won five straight games across three competitions, including Wednesday's penalty shootout victory over Chelsea to reach the League Cup quarter-finals.
Fourth-placed Liverpool are six points behind Arsenal.
"It's still October, take one game at a time and I always say the first reference is normally when we have played against each other once, halfway through the season, and then you can start looking at the standings," Iraola told reporters.
"Now we are in a position where we need to improve, keep getting better. Can fans dream? It's good if they have expectations and think we can win. But if you ask me, it is still early."
Good record against Arsenal
Iraola has a good record against Arsenal having won three of his last four meetings with Mikel Arteta's side as Bournemouth head coach.
With Arsenal chasing a first win at Anfield since 2012, the Spaniard said past records would count for little.
"It is true we had good results against them with Bournemouth but it does not mean a lot as it is a totally different team, different group of players, different moments," he said.
"At the end of the day it is about winning the duels, running more than them, winning the aerial duels, set plays, mini games, these things that you have to control against Arsenal. They are the champions, they are top of the league right now, they have only lost one game this season."
Sunday's match offers Iraola the chance to meet up with his former teammate Arteta after they came through the youth ranks together in San Sebastian in Spain's Basque Country.
"Last week was (Chelsea boss) Xabi (Alonso), now Mikel, a lot of former friends on the opposition bench lately. I think it is a good thing in terms of spending 5-10 minutes after the game normally with them," Iraola said.
Dominik Szoboszlai (hamstring) and Victor Munoz (knee) could feature after recovering from injuries.
English Premier League
The 2026/27 Premier League season is underway. From reports and analysis to all the big breaking news, Flashscore is your one-stop shop to keep up with all the drama from the world's most-followed football league.